3.5 Trigonometry (A-level only)

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Question 139

The angular displacement of a pendulum, $Θ\Theta$ , is modelled by the function $Θ(t)=cos⁡t\Theta(t) = \cos t$ , where $t$ is the time in seconds measured from the equilibrium position. A specific displacement $p$ is recorded at time $\phi$ , where $\phi < \frac{\pi}{2}$ , such that $cos⁡ϕ=p\cos \phi = p$ .

State, in terms of $p$ , the value of: (i) $\cos (2\pi - \phi)$ (ii) $cos⁡(ϕ−π)\cos (\phi - \pi)$ (iii) $\cos (-\phi)$

[3]

Sketch the graph of $\cos 2t$ for the interval $\le t \le \pi$ , labelling the coordinates of the points where the curve meets the axes and any stationary points.

[2]

Determine, in terms of $ϕ\phi$ , the $t$ -coordinates of any points in the interval $\pi$ for which $cos⁡2t=p\cos 2t = p$ .

[2]

3.5 Trigonometry (A-level only)

Question 139

State, in terms of $p$ , the value of: (i) $\cos (2\pi - \phi)$ (ii) $cos⁡(ϕ−π)\cos (\phi - \pi)$ (iii) $\cos (-\phi)$

[3]

Sketch the graph of $\cos 2t$ for the interval $\le t \le \pi$ , labelling the coordinates of the points where the curve meets the axes and any stationary points.

[2]

Determine, in terms of $ϕ\phi$ , the $t$ -coordinates of any points in the interval $\pi$ for which $cos⁡2t=p\cos 2t = p$ .

[2]

3.5 Trigonometry (A-level only)

Question 139

Markscheme

3.5 Trigonometry (A-level only)

Question 139

Markscheme

3.5 Trigonometry (A-level only)

Question 139

3.5 Trigonometry (A-level only) Questions

3.5 Trigonometry (A-level only)

Question 139

3.5 Trigonometry (A-level only) Questions